A paradigm to test parallel and serial models, capable of being applied in a number of experimental contexts has recently been reported. The serial models presently covered by the paradigm make almost no distributional assumptions. The comparable parallel models are somewhat less general, being based on distributions arising from exponential intercompletion times, thus giving rise to general gamma processes. The first aim of the proposed research is to generalize the parallel class of models beyond this limitation. The second aim is to explore questions related to hypothesis with the paradigm. In particular, reasonable sets of distribution and parameter values will be compared with and related to the number of observations required for statistical significance.